Is there a two-qudit Choi entanglement witness $W^{(+)}$?

Example 2 in arXiv:1811.09896 states that the "Choi EW (entanglement witness) $W^{(+)}$ obtained from the Choi map in $d=3$ $ldots$ is given by
begin{equation}
W^{(+)} = frac{1}{6} left( sum_{i=0}^{2} [ 2| ii rangle langle ii | + | i,i-1 rangle langle i, i-1 | ] – 3 mathrm{P}_{+} right) nonumber,
end{equation}
where $mathrm{P}_+ = |phi^+rangle langle phi^+|$ with the Bell state $|phi^+rangle = (|00rangle + |11rangle + |22rangle) / sqrt{3}$." It is noted that this is applicable in the two-qutrit ($9 times 9$ density matrix) setting.

I would like to know – if it exists – a two-qudit analogue, applicable to $16 times 16$ density matrices. If it does, I presume the summation would run from 0 to 3, and the $sqrt{3}$ in the new (obvious) Bell state formula be replaced by 2. Might the coefficient 2 be replaced by 3, and the $3 P_+$ by $4 P_+$? The $frac{1}{6}$ does not seem of particular importance for testing purposes.

However, the last paragraph of arXiv:1105.4821 strongly suggests that there is no simple/direct two-qudit analogue.